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3 years ago

What is factor form x^2-10x+25 show work

Mathematics

1 answer:

iogann1982 [59]3 years ago

5 0

This trinomial is in a special form that can

be factored as the product of two binomials.

The first term in each binomial will be a factor of the x² term.

Since x² is just x · x, we use those as our first factors.

To factor this trinomial, we need factors of our constant that

add to the coefficient of the middle term in our trinomial.

So we're looking for factors of 25 that add to -10.

When your constant is positive and your middle term is negative,

you are going to use the negative factors of your constant term.

So the two numbers hat multiply to gives

us 25 and add to -10 are -5 and -5.

So our answer is (x - 5)(x - 5).

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{x^2+6x-27/x^2-9x+18<br> how to solve step by step

Alika [10]

Answer:

Step-by-step explanation:

Step by Step Solution:

More Icon

STEP

Simplify ———————

x2 - 81

Trying to factor as a Difference of Squares:

1.1 Factoring: x2 - 81

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 81 is the square of 9

Check : x2 is the square of x1

Factorization is : (x + 9) • (x - 9)

Equation at the end of step

(((x2)-18x)+81) 5

———————————————•———————————

(((x2)-6x)-27) (x+9)•(x-9)

STEP

x2 - 18x + 81

Simplify —————————————

x2 - 6x - 27

Trying to factor by splitting the middle term

2.1 Factoring x2 - 18x + 81

The first term is, x2 its coefficient is 1 .

The middle term is, -18x its coefficient is -18 .

The last term, "the constant", is +81

Step-1 : Multiply the coefficient of the first term by the constant 1 • 81 = 81

Step-2 : Find two factors of 81 whose sum equals the coefficient of the middle term, which is -18 .

-81 + -1 = -82

-27 + -3 = -30

-9 + -9 = -18 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -9

x2 - 9x - 9x - 81

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-9)

Add up the last 2 terms, pulling out common factors :

9 • (x-9)

Step-5 : Add up the four terms of step 4 :

(x-9) • (x-9)

Which is the desired factorization

Trying to factor by splitting the middle term

2.2 Factoring x2-6x-27

The first term is, x2 its coefficient is 1 .

The middle term is, -6x its coefficient is -6 .

The last term, "the constant", is -27

Step-1 : Multiply the coefficient of the first term by the constant 1 • -27 = -27

Step-2 : Find two factors of -27 whose sum equals the coefficient of the middle term, which is -6 .

-27 + 1 = -26

-9 + 3 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 3

x2 - 9x + 3x - 27

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-9)

Add up the last 2 terms, pulling out common factors :

3 • (x-9)

Step-5 : Add up the four terms of step 4 :

(x+3) • (x-9)

Which is the desired factorization

Canceling Out :

2.3 Cancel out (x-9) which appears on both sides of the fraction line.

Equation at the end of step

(x - 9) 5

——————— • —————————————————

x + 3 (x + 9) • (x - 9)

STEP

Canceling Out

3.1 Cancel out (x-9) which appears on both sides of the fraction line.

Final result :

—————————————————

(x + 3) • (x + 9)

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